Uke can only be either in motion or stationary. If uke is in motion there's no need for me to move him. If uke is stationary, again, there's no need for me to move him.
Uke can only attack while he's moving. Since he's moving there's no need for me to move him.
Uke attacks and stops, remaining motionless. Since he's not moving he's not attacking and there's no need for me to move him.
(Original blog post may be found here
Invalidated very simply - attacker is standing motionless, but his position is preventing me from reaching a desired goal. For example, assisting a friend who is being assaulted by the attacker's compatriot.
Also it assumes that anything moving is, but it's very nature, unstable. That is not, as Gary pointed out, always the case.
This is the kind of thing that I heard a lot of when I first started Aikido - seems to make sense, but upon examination you find that there are just too many situations where it just doesn't hold up.